Mechanics question help needed

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A goods train consists of an engine of mass 40 tonnes and two trucks of mass 20 tonnes each. The engine is producing a driving force of 50000N, causing the train to accelerate. The ground is level and resistance force may be neglected.

(i) By considering the motion of the whole train, find its acceleration.
(ii) Draw a diagram to show the forces acting on the engine and use this to help you find the tension in the first coupling.
(iii) Find the tension in the second coupling.

The brakes on the first truck are faulty and suddenly engage, causing a resistance of 10000N

(iv) What effect does this have on the tension in the coupling to the last truck?


Parts (i) to (iii) I'm fine with and got a=0.625ms^2 and T2=12500N.

I have no clue how to get the answer of 10000N to part (iv). I've tried tons of stuff.When cart 1 brakes the acceleration as a whole obviously changes, which I try to calculate but whatever value I get it always gives me an incorrect tension. I've been making three simultaneous equations of motion (one from engine, two from each cart) and finding each value but nothing works whatever mass I use.

E.g. Equations of motion (engine, cart 1, cart 2)
• 50000N - T1 = 80000a
• T2 - (T1 + 10000N) = 60000a (I've used all possible mass values here but 60000 is most likely correct (cart and engine), including 20000 (cart alone), 80000 (whole thing), 40000 (both carts).
• T2 = 20000a

This is long post I know but this question is really stressing me out and it's probably just something stupid that I'm missing

Assuming that your first equation is supposed to be just about the engine, it should be 40000a.

Your second equation is a mess (sorry, that's a bit harsh). If it is supposed to be just about the first truck, it should be T1 - (T2 + 10000) = 20000a.

However, I would do this last part in the same way as you did the earlier parts, i.e. consider the whole train:
50000 - 10000 = 80000a

Assuming that your first equation is supposed to be just about the engine, it should be 40000a.

Your second equation is a mess (sorry, that's a bit harsh). If it is supposed to be just about the first truck, it should be T1 - (T2 + 10000) = 20000a.

However, I would do this last part in the same way as you did the earlier parts, i.e. consider the whole train:
50000 - 10000 = 80000a